Recently, the proposed van der Waals (vdW) equation of state
accounting for
the quantum statistics (QS) [1]}, [2]}, [3]}
was used to describe the
properties of
hadronic matter, also with many component extensions and applications to the
fluctuation calculations for different thermodynamical averages
[4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.
The role and size of the effects of
QS was studied analytically for nuclear matter, also
for pure neutron and pure \(\alpha \) -particle matter in Ref. [3]}.
Particularly,
we investigated a dependence
of the critical point parameters on
the particle mass \(m\) ,
degeneracy factor \(g\) , and the
vdW parameters \(a\)  and \(b\) 
which describe particle interactions for
each of these systems.
Our consideration
was restricted to small temperatures,
\(T \;\hbox{\hspace{1.00006pt}$\sim $} \hspace{-11.19995pt}\) <\(\)  30\(~MeV, and not too largeparticle densities. Within these restrictions, thenumber of nucleonsbecomes a conserved number,and the chemical potential ofsuch systems regulates the number density ofparticles. An extension to the fully relativistic hadron resonances in a gasformulation withvdW interactions betweenbaryons and between antibaryons was considered inRef.~\cite {VGS-17}.An application of this extended model to net baryon number fluctuationsin relativistic nucleus-nucleuscollisions was developed in Ref.~\cite {VJGS-18}.We do not include the Coulomb forcesand make no differences between protons and neutrons(both these particles are named as nucleons).In addition, under these restrictions thenon-relativistic treatment becomes very accurateand is adopted in our studies. In the present work we are going to applythe same analytical method as in Ref.~\cite {FMG19} to themixed two-componentsystem of nucleons and \)\( particles. Another attractive subject ofthis work is to apply our analytical results to analysis of theparticle number fluctuations near the critical points ofthe nuclear matter.\)
